A LAPLACE TRANSFORM PAIR MODEL TO DETERMINE BREMSSTRAHLUNG SPECTRA FROM ATTENUATION DATA (RADIATION, X-RAY, SPECTRAL MODELING)

Every x-ray attenuation curve inherently contains all the information necessary to extract the complete energy spectrum of a beam. To date, attempts to obtain accurate spectral information from attenuation data have been inadequate.^ This investigation presents a mathematical pair model, grounded in physical reality by the Laplace Transformation, to describe the attenuation of a photon beam and the corresponding bremsstrahlung spectral distribution. In addition the Laplace model has been mathematically extended to include characteristic radiation in a physically meaningful way. A method to determine the fraction of characteristic radiation in any diagnostic x-ray beam was introduced for use with the extended model.^ This work has examined the reconstructive capability of the Laplace pair model for a photon beam range of from 50 kVp to 25 MV, using both theoretical and experimental methods.^ In the diagnostic region, excellent agreement between a wide variety of experimental spectra and those reconstructed with the Laplace model was obtained when the atomic composition of the attenuators was accurately known. The model successfully reproduced a 2 MV spectrum but demonstrated difficulty in accurately reconstructing orthovoltage and 6 MV spectra. The 25 MV spectrum was successfully reconstructed although poor agreement with the spectrum obtained by Levy was found.^ The analysis of errors, performed with diagnostic energy data, demonstrated the relative insensitivity of the model to typical experimental errors and confirmed that the model can be successfully used to theoretically derive accurate spectral information from experimental attenuation data. ^

Clinical factors associated with growth and mortality of pediatric patients on HAART at Mulago PIDC, Uganda, 2003--2006

The global social and economic burden of HIV/AIDS is great, with over forty million people reported to be living with HIV/AIDS at the end of 2005; two million of these are children from birth to 15 years of age. Antiretroviral therapy has been shown to improve growth and survival of HIV-infected individuals. The purpose of this study is to describe a cohort of HIV-infected pediatric patients and assess the association between clinical factors, with growth and mortality outcomes. ^ This was a historical cohort study. Medical records of infants and children receiving HIV care at Mulago Pediatric Infectious Disease Clinic (PIDC) in Uganda between July 2003 and March 2006 were analyzed. Height and weight measurements were age and sex standardized to Centers for Disease Control and prevention (CDC) 2000 reference. Descriptive and logistic regression analyses were performed to identify covariates associated with risk of stunting or being underweight, and mortality. Longitudinal regression analysis with a mixed model using autoregressive covariance structure was used to compare change in height and weight before and after initiation of highly active antiretroviral therapy (HAART). ^ The study population was comprised of 1059 patients 0-20 years of age, the majority of whom were aged thirteen years and below (74.6%). Mean height-for-age before initiation of HAART was in the 10th percentile, mean weight-for-age was in the 8th percentile, and the mean weight-for-height was in the 23rd percentile. Initiation of HAART resulted in improvement in both the mean standardized weight-for-age Z score and weight-for-age percentiles (p <0.001). Baseline age, and weight-for-age Z score were associated with stunting (p <0.001). A negative weight-for-age Z score was associated with stunting (OR 4.60, CI 3.04-5.49). Risk of death decreased from 84% in the >2-8 years age category to 21% in the >13 years age category respectively, compared to the 0-2 years of age (p <0.05). ^ This pediatric population gained weight significantly more rapidly than height after starting HAART. A low weight-for-age Z score was associated with poor survival in children. These findings suggest that age, weight, and height measurements be monitored closely at Mulago PIDC. ^

Analyzing left-truncated right-censored data with uncertain onset time with parametric models

Prevalent sampling is an efficient and focused approach to the study of the natural history of disease. Right-censored time-to-event data observed from prospective prevalent cohort studies are often subject to left-truncated sampling. Left-truncated samples are not randomly selected from the population of interest and have a selection bias. Extensive studies have focused on estimating the unbiased distribution given left-truncated samples. However, in many applications, the exact date of disease onset was not observed. For example, in an HIV infection study, the exact HIV infection time is not observable. However, it is known that the HIV infection date occurred between two observable dates. Meeting these challenges motivated our study. We propose parametric models to estimate the unbiased distribution of left-truncated, right-censored time-to-event data with uncertain onset times. We first consider data from a length-biased sampling, a specific case in left-truncated samplings. Then we extend the proposed method to general left-truncated sampling. With a parametric model, we construct the full likelihood, given a biased sample with unobservable onset of disease. The parameters are estimated through the maximization of the constructed likelihood by adjusting the selection bias and unobservable exact onset. Simulations are conducted to evaluate the finite sample performance of the proposed methods. We apply the proposed method to an HIV infection study, estimating the unbiased survival function and covariance coefficients. ^